"Educated people in Moscow spoke Latin.
"
This wasn't the common case and was not the reason for the land to be called Third Rome.
"Like Rome, Moscow was located near trade routes."
Also not the case. Moscow was in a harsh location.
The only one that could be is the following:
The Russians called their leaders tsar, the Russian word for “Caesar.”
The first one to call Moscow "The third rome" was the Monk Philotheos. So this was not the case.
The actual answer is:
Moscow was the center of expanding political power.
Just like what Philoteus called "the first Rome" which was the original one and "the second Rome" which was Constantinopla, the now so called "Third Rome" was at the center of an expending political power and Moscow should be the successor of Constantinopla.
